First compiled in 1986, SENSEX(Sensitive Index) is a basket of 30 constituent stocks representing a sample of large, liquid and representative companies. The base year of SENAEX is 1978-79 and the base value ie 100. The index widely reported in both domestic and international markets through print as well as electronic media everyday. SENSEX had touched the 10000 landmark in February 2006 and has come within the first three indices in the world in terms of rapid up-down movement. So far as the authors are aware, apporopriate powerful models to generate accurate forecasts of SENSEX values are not available in the literature. In this paper the SENSEX monthly highest time-series data from the period, January 1999 to December 2006, have been used to model the monthly highest values of the SENSEX and to generate future forecasts for the subsequent twelve months till December 2007. The special features of this model.([ARIMA(1,1,6)×(1,0,3)₁₂] selected from among fifty competitive models) are that the forecasts are very close to the future values realized later in January 2007. It had predicted that the SENSEX would touch 1400 landmark in the month of Jnanuary 2007 which, indeed, was the scene. So it can be expected that the remaining forecasts on monthly highest values will also be idential with those SENSEX values representing the real situations destined to prevail in future. The most salient feature is that the R value is found to be 0.983 which indicates that the prediction power of the model is very high, thouge only 96 monthly SENSEX values have been used for prediction and 3 monthly SENSEX values have been reserved for determination of the accuracy of the forecast model.